Power tail asymptotic results of a discrete time queue with long range dependent input

Abstract

In this paper, we consider a discrete time queueing systemfed by a superposition of an ON and OFF source with heavy tail ON periods andgeometric OFF periods and a D-BMAP (Discrete Batch Markovian Arrival Process).We study the tail behavior of the queue length distribution andboth infinite and finite buffer systems are considered. In the infinitebuffer case, we show that the asymptotic tail behavior of the queue length of thesystem is equivalent to that of the same queueing system with the D-BMAP being replaced bya batch renewal process.In the finite buffer case (of buffer size K), we deriveupper and lower bounds of the asymptoticbehavior of the loss probability as K rightarrow infty.